On a Connection between Kernel PCA and Metric Multidimensional Scaling

This leads to a metric MDS algorithm where the desired configuration of points is found via the solution of an eigenproblem rather than through the iterative optimization of the stress objective function. The question of kernel choice is also discussed. 1 Introduction Suppose we are given n objects, and for each pair (i,j) we have a measurement of the "dissimilarity" Oij between the two objects. In multidimensional scaling (MDS) the aim is to place n points in a low dimensional space (usually Euclidean) so that the interpoint distances dij have a particular relationship to the original dissimilarities. In classical scaling we would like the interpoint distances to be equal to the dissimilarities. For example, classical scaling can be used to reconstruct a map of the locations of some cities given the distances between them.